Very Low Drag Aerospike Projectile

ABSTRACT

A projectile is provided for firing from a launcher, including an ogive nose; a cylindrical midsection joined to the nose; and a base curvature shaped as a modified aerospike nozzle. The aerospike base is created using a modified method of characteristics nozzle design process. The aerospike base allows for the efficient expansion of air behind the projectile to recover base pressure and reduce the overall drag of the projectile.

CROSS REFERENCE TO RELATED APPLICATION

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STATEMENT OF GOVERNMENT INTEREST

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BACKGROUND

The invention relates generally to a projectile having a base, or rear,section designed as a modified inverted short bell nozzle commonlyreferred to as aerospike design.

SUMMARY

A projectile with an aerospace base design, such that a projectile isprovided for firing from a launcher, including an ogive nose; acylindrical midsection joined to the nose; and concave curvature basewith the shape of a modified inverted short bell nozzle.

BRIEF DESCRIPTION OF THE DRAWINGS

These and various other features and aspects of various exemplaryembodiments will be readily understood with reference to the followingdetailed description taken in conjunction with the accompanyingdrawings, in which like or similar numbers are used throughout, and inwhich:

FIG. 1 is an elevation view of a comparative projectiles.

FIG. 2 is an isometric view of a comparative projectiles;

DETAILED DESCRIPTION

In the following detailed description of exemplary embodiments of theinvention, reference is made to the accompanying drawings that form apart hereof, and in which is shown by way of illustration specificexemplary embodiments in which the invention may be practiced. Theseembodiments are described in sufficient detail to enable those skilledin the art to practice the invention. Other embodiments may be utilized,and logical, mechanical, and other changes may be made without departingfrom the spirit or scope of the present invention. The followingdetailed description is, therefore, not to be taken in a limiting sense,and the scope of the present invention is defined only by the appendedclaims.

The shape of a projectile is critical in determining how it flies. Theflow of air around the base of the projectile is the most critical indetermining the overall drag on the projectile. Because of the lack ofaccurate theoretical models of this flow, the base is one of the leaststudied and innovated parts of the projectile. A new base design basedon a modified inverted rocket nozzle design method commonly called theshort bell nozzle design based upon the method of characteristics isproposed to improve on projectile performance.

The aerodynamic drag force on a supersonic projectile can be dividedinto three components; wave, friction, and base drag. The wave drag isdue to the oblique shockwave that is created in front of the projectile.This component of drag is relatively well understood and can beevaluated with simple shock-expansion theory, computational fluiddynamics (CFD), or wind tunnel testing. With these multiple methods ofdesign, the shape of the nose of a projectile (the ogive) is welldesigned.

The friction drag is caused by viscosity in the air and is wellunderstood with modern boundary layer theory. This theory dictates thesmooth skin of the projectile and competes with stability considerationsto determine the overall length of the projectile.

Base drag can be summed up by the d'Alembert's paradox. In a perfectinviscid fluid, a projectile should have no drag due to the ‘recovery’of pressure on the back side of the projectile perfectly balancing thepressure on the front of the projectile. Real projectiles only partiallyrecover the base pressure and the difference between the front pressureand the back pressure is called base drag.

Although extensive empirical models have been proposed to calculate basedrag, no theoretical model exists that explain the phenomena. See D. R.Chapman: “An Analysis of Base Pressure at Supersonic Velocities andComparison with Experiment”, NACA Report 1051, 1951 (available athttps://digital.library.unt.edu/ark://167531/metadc65505/m2/1/high_res_d/19930090963.pdf).See W. K. Lockman: “Free-Flight Base Pressure and Heating Measurementson Sharp and Blunt Cones in a Shock Tunnel”, AIAA Journal, October 1967.See B. M. Bulmer: “Study of Base Pressure in Laminar Hypersonic Flow,Re-entry Flight Measurements”, AIAA Journal, October 1975.

The method of characteristics is a mathematical method for the solutionof hyperbolic partial differential equations (PDE). The flow of air canbe modeled using the Euler equation which for supersonic flow is ahyperbolic PDE. A common use of the method of characteristics with theEuler equation is the design of supersonic nozzles to efficiently expandthe exhaust gasses out of a rocket motor. It is often desirable to havethe shortest nozzle possible to expand the gasses from approximatelyMach 1 at the throat of the rocket motor to the design exit Mach numberof approximately Mach 3. The resulting nozzle design is called the shortbell nozzle or minimum length nozzle design.

An aerospike rocket nozzle is an inverted (inside-out) short bell nozzlewhere the nozzle curvature is designed and then inflected about theinlet wall axis. The exhaust gasses exit from a ring around the edge ofspike and expand over the surface. Due to the effect of compressiblegasses called choked flow, the gasses exit again at approximately Mach 1and are expanded to approximately Mach 3.

FIG. 1 and FIG. 2 shows a graphical view of a projectile with anexemplary aerospike base. The short bell nozzle design method wasmodified to allow for inlet Mach numbers higher than 1 to match the Machnumber that commonly is seen entering the base flow section of aprojectile. For this embodiment, the Mach number entering the base wastaken as Mach 2 and the exit was set at Mach 3. The aerospike baseisentropically (efficiently) expands the flow around the base to recoveras much pressure as possible between the inlet and exit Mach numbers.

The curvature of the aerospike base can be further modified to accountfor the viscous boundary layer. This technique is common in the designof airfoils and slightly adjusts the outline of the airfoil to accountfor the viscous sub-layer of flow as a boundary wall.

These exemplary embodiments employ the exemplary method to designprojectile bases so that the flow does not separate into a recirculationzone behind the projectile but is carefully compressed after flow aroundthe edge of the base. The increase in base pressure reduces the basedrag and therefore the overall drag of the projectile.

This projectile design could potentially be used in every sizedprojectile to reduce drag and increase accuracy from small arms forcivilian or military use to large caliber artillery and naval guns.

The aerospike base has the additional benefit of streamlining theprojectile for low Mach number flow and reducing the base drag for thiscase as well. The projectile with the aerospike base is improved overall Mach numbers as the projectile is slowed from the initial velocityuntil impact.

While certain features of the embodiments of the invention have beenillustrated as described herein, many modifications, substitutions,changes and equivalents will now occur to those skilled in the art. Itis, therefore, to be understood that the appended claims are intended tocover all such modifications and changes as fall within the true spiritof the embodiments.

What is claimed is:
 1. A projectile for firing from a launcher, saidprojectile comprising: a fore nose; a cylindrical midsection joined tosaid nose; and a base curvature shaped as a modified aerospike nozzle.2. The projectile according to claim 1, wherein said nose is an ogive.3. The projectile according to claim 1, wherein the projectile containsexplosives and fuse.
 4. The projectile according to claim 1, wherein theprojectile is spin stabilized by launch from a rifled launcher.
 5. Theprojectile according to claim 1, wherein the projectile material isselected from the group consisting of copper or copper alloy-jacketedlead, tungsten, tantalum, alloys thereof and composites thereof.
 6. Theprojectile according to claim 1, wherein said nose is a hollow point. 7.The projectile according to claim 1, wherein the projectile is launchedin a sabot configuration.
 8. The projectile according to claim 1,wherein the flat end of said base is filled with energetic material toilluminate the trajectory of the projectile (tracer).
 9. The projectileaccording to claim 1, wherein the projectile is mounted into a bulletcase.
 10. The projectile according to claim 1, wherein the basecurvature is approximated as an aerospike by a polynomial, exponential,inverse power series, or trigonometric mathematical models.
 11. Theprojectile according to claim 1, wherein the base curvature is correctedfrom the modified short bell nozzle curvature by application of boundarylayer theory to offset the curvature by the thickness of the viscousboundary layer created by the interaction of the air with the curvature.